189 ,S7 I Copy 1 EXPERIMENTS IN FIELD PLOT TECHNIC FOR THE PRELIMINARY DETERMINATION OF COMPARATIVE YIELDS IN THE SMALL GRAINS BY Lewis John Stadler, B. S. A., A. M. Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF MISSOURI COLUMBIA, MISSOURL 192L EXPERIMENTS IN FIELD PLOT TECHNIC FOR THE PRELIMINARY DETERMINATION OF COMPARATIVE YIELDS IN THE SMALL GRAINS BY Lewis John Stabler, B. S. A., A. M. Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF MISSOURI COLUMBIA, MISSOURI. 1921. UNIVERSITY OF MISSOURI S"^ COLLEGE OF AGRICULTURE Agricultural Experiment Station BOARD OF CONTROL, THE CURATORS OF THE UNIVERSITY OF MISSOURI E. LANSING RAY, St. Eouis EXECUTIVE BOARD OF THE UNIVERSITY P. E. BURTON, Joplin H. J. BLANTON, Paris ADVISORY COUNCIL THE MISSOURI STATE BOARD OF AGRICULTURE OFFICERS OF THE STATION F. B. MUMFORD, M. S., DIRECTOR J. C. JONES, Ph. D., LL.D., PRESIDENT OF THE UNIVERSITY STATION STAFF DECEMBER, 1921 AGRICULTURAL CHEMISTRY C. R. MouLTON, Ph. D. L. D. Haigh, Ph. D. W. S. Ritchie, A. M. E. E. Vanatta, M. S. A. R. Hall, B. S. in Agr. E. G. SiEvEKiNG, B. S. in Agr. AGRICULTURAL ENGINEERING J. C. WOOLEY, B .S. Mack M. Jones, B. S. ANIMAL HUSBANDRY E. A. Trowbridge, B. S. in Agr. L. A. Weaver, B. S. in Agr. A. G. HoGAN, Ph. D. F. B. MuMFORD, M. S. D. W. Chittenden, B. S. in Agr. A. T. Edinger, B. S. in Agr. H. D. Fox, B. S. in Agr. BOTANY W. J. Robbins, Ph. D. E. F. Hopkins, Ph. D. DAIRY HUSBANDRY A. C. RagsdalE. B. S. in J^gr. W. W. Swett, A. M. Wm. H. E. Reid, a. M. Samuel Brody, M. A. C. W. Turner, B. S. in Agr. D. H. Nelson, B. S. in Agr. ENTOMOLOGY Leonard Haseman, Ph. D. K. C. Sullivan, A. M. O. C. McBride, FIELD CROPS W. C. Etheridge, Ph. D. C. A. Helm, A. M. L. J. Stadler, a. M. O. W. Letson, B. S. in Agr. B. M. King, B. S. in Agr. A. C. Hill, B. S. in Agr. Miss Bertha C. Hite, A. B.> Miss Pearl Drummond, A. A.* RURAL LIFE O. R. Johnson, A. M. S. D. Gromer, a. M. E. L- Morgan, A. M. Ben H. Frame, B. S. in Agr. HORTICULTURE V. R. Gardner, M. S. A. H. D. Hooker, Jr., Ph. D. J. T. Rosa, Jr., M. S. F. C. Bradford, M. S. H. G. Swartwout, B. S. in Agr. POULTRY HUSBANDRY H. L. Kempster, B. S. Earl W. Henderson SOILS M. F. Miller, M. S. A. H. H. Krusekopf, a. M. W. A. Albrecht, Ph. D. F. L. DuLEY, A. M.^* R. R. Hudelson, a. M. Wm. DeYoung, B. S. in Agr. H. V. Jordan, B. S. in Agr. Richard Bradfield, A. B. O. B. Price, B. S. in Agr. VETERINARY SCIENCE J. W. CONNAWAY, D. V. S., M. D. L. S. Backus, D. V. M. O. S. Crisler, D. V. M. A. J. DuRANT, A. M. H. G. Newman, A. M. OTHER OFFICERS R. B. Price, M. S., Treasurer Leslie Cowan, B. S., Sercretary S. B. Shirkey, a. M., Asst. to Director A. A. Jeffrey, A. B., Agricultural Editor J. F. Barham, Photographer Miss Jane Frodsham, Librarian E. E. Brown, Business Manager Hn service of U. S. Department of Agriculture, Seed Testing Laboratory. ^On leave of absence. ». ._^...,— ' , ■:■ \ LIBf^Afr^.OF CONGRE39 CONTENTS Page The Problem 6 Plan and Method of Investigation 9 Terminology 9 Procedure 11 Work of 1919 12 Work of 1920 16 Work of 1921 18 Competition as a Source of Error in Preliminary Tests 23 Previous Investigation 23 Experimental Results 25 Illustrations of Eflfects of Competition 26 Relation of Competition to Various Characteristics of the Com- peting Varieties 31 Discussion 40 Size and Replication of Plots 43 Previous Investigation 43 Experimental Results 44 Size of Plots 44 RepHcation of Plots 50 Adjustment of Yields by Means of Check Plots 54 Previous Investigation 54 Experimental Results 56 Method Used in Adjusting Yields 58 Relative Variability of Actual and Adjusted Yields 60 Difference in Results Obtained by Adjustment with Different Check Varieties 63 Value and Limitations of Adjusting Yields by Means of Check Plots 71 Concluding Remarks 12) Summary 75 Acknowledgment 11 References Cited 78 TABLES Table Number Table Page 1 Yields of Barley Varieties 1919 13 2 Yields of Oats Varieties 1919 14 3 Yields of Oats Strains 1919 15 4 Yields of Wheat Varieties 1920 16 5 Yields of Wheat Varieties 1921 17 6 Yields of Wheat Varieties and Mixtures 1921 18 7 Yields of Oats Varieties 1921 21 8 Yields of Oats Strains 1921 22 9 Relative Yields of Two Small Grain Varieties When Compared in Al- ternate Rows and in Blocks (Kiesselbach) 24 10 Correlation of Competition with Various Characteristics in Barley Va- riety Test 1919 35 11 Correlation of Competition with Various Characteristics in Oats Va- riety Test 1919 35 4 Tables 12 Correlation of Competition with Various Characteristics in Oats Strain Test 1919 36 13 Correlation of Competition with Various Characteristics in Wheat Va- riety Test 1920 n 14. Correlation of Competition with Various Characteristics in Wheat Va- riety Test 1921 Z1 15 Correlation of Competition with Various Characteristics in Wheat Mix- ture Test 1921 38 16 Correlation of Competition with Various Characteristics in Oats Va- riety Test 1921 39 17 Summary of Effects of Competition in All Tests 41 18 Correlation of Yield with Dates of Heading and Maturity in Variety Tests of Barley, Oats, and Wheat 42 19 Yield and Variability of 1-row, 3-row, and 5-row Check Plots in Bar- ley Variety Test 1919 45 20 Yield and Variability of 1-row, 3-row, and 5-row Check Plots in Oats Variety Test 1919 46 21 Yield and Variability of 1-row, 3-row, and 5-row Check Plots in Oats Strain Test 1919 47 22 Yield and Variability of 1-row, 3-row, and 5-row Check Plots in Wheat Variety Test 1920 47 23 Yield and Variability of 3-row and 5-row Check Plots in Wheat and Oats Test 1921 48 24 Yield and Variability of 3-row and 5-row Test Plots in All Tests 50 25 Relation of Plot Variability to Size of Experiment Field in Wheat Va- riety Test 1920 51 26 Relation of Plot Variability to Size of Experiment Field in Wheat Va- riety Test 1921 52 27 Relation of Plot Variability to Size of Experiment Field in Oats Va- riety and Strain Tests 1921 52 28 Soil Heterogeneity of an Experiment Field as Determined from Yields of Two Check Varieties 53 29 Effect on Plot Variability of Adjusting Yields by Check Plots (Kies- selbach ) 55 30 Reduction of Variability by the Use of Check Plots Equivalent to That Probably Attainable with the Same Number of Plots by Replication . 57 31 Relative VariabiHty of Actual and Adjusted Yields in Barley Variety Test 1919 59 32 Relative Variability of Actual and Adjusted Yields in Oats Variety Test 1919 60 i2) Relative Variability of Actual and Adjusted Yields in Oats Strain Test 1919 61 34 Relative Variability of Actual and Adjusted Yields in Wheat Variety Test 1920 62 35 Relative Variability of Actual and Adjusted Yields in Wheat Variety Test 1921 64 36 Relative Variability of Actual and Adjusted Yields in Wheat Mixture Test 1921 65 Zl Relative Variability of Actual and Adjusted Yields in Oats Variety Test 1921 66 38 Relative Variability of Actual and Adjusted Yields in Oats Strain Test 1921 67 39 Relative Variability of Actual and Adjusted Yields of Kherson and Red Rustproof Oats Each in 120 Distributed Plots, in Oats Variety and Strain Tests 1921 68 40 Summary of Relative Variability of Actual and Adjusted Yields of Interior Rows in All Tests 1921 71 EXPERIMENTS IN FIELD PLOT TECHNIC FOR THE PRELIMINARY DETERMINA- TION OF COMPARATIVE YIELDS IN THE SMALL GRAINS L. J. Stadler During recent years the investigation of the reliability of field experiments has become an important phase of agronomic research. Field experiments as ordinarily conducted have been shown to be affected by many gross errors. In the light of these investigations it has become apparent that the results of many of the older experiments are inconclusive or even misleading. Various expedients have been suggested for counteracting experimental error. Some of these have been quite successful, while others have probably done more harm than good. The pioneer investigations in this field have been of great value in directing attention to the important sources of error and in suggesting possible means for their control. Doubtless at the present time most of the major sources of error are recognized. But the true extent of the errors and the actual practical value of the methods of counteracting them can be determined only by numerous investiga- tions of experimental methods under different conditions. The present paper is concerned with experimental error and field plot technic in preliminary variety and strain tests with the small grains. The same type of test is extensively used in small grain im- provement, not only in the preliminary testing of varieties, but also in the comparison of strains and selections. Although the small plot test is particularly subject to errors of certain sorts, it has a decided advantage over tests in larger plots in the possibility of extensive replication, which is probably the greatest single factor in the reduc- tion of experimental error. It should be possible, consequently, to obtain extremely accurate results in small plot tests without the use of large experimental areas, when the errors peculiar to the small plot are understood and controlled. (5) 6 Missouri Agr. Exp. Sta. Research Bulletin 49 THE PROBLEM. At present the type of plot most commonly used for the pre- liminary testing of small grain varieties and strains is probably the "rod-row." The methods of conducting rod-row tests described by Love and Craig' may be considered typical. The varieties or strains are sown by hand in rows one foot apart, usually opened and covered with a wheel hoe or similar implement. The seed for each row is weighed out in a quantity equivalent to ordinary rates of seeding in field practice. In harvesting, six inches or a foot at the end of the row is discarded, to prevent increase in yield by reason of the more favorable space conditions at the ends of the rows. The list of va- rieties is repeated in several series, and the results averaged to reduce the error from plot variability. A check variety is grown in every tenth row to indicate the variability of the field. The use of rod-row tests involves several errors, derived principally from the modified conditions under which the plants are grown. The object of the test is to discover the relative value of the strains under field conditions, and therefore any modification of field conditions which may favor some sorts more than others introduces error. The wide spacing between rows, with consequently heavier seeding in the row for any given rate of planting; the hand seeding and covering, re- sulting usually in slightly ridged rather than slightly furrowed rows ; and the growing of different varieties in single rows, in competition with other varieties rather than with their own kind, are examples of typical conditions which may be expected to favor some varieties more than others. Consequently the best varieties in the rod-row test are not necessarily the best varieties under field culture, even when soil and seasonal variability are reduced to the minimum by replication of plots and repetition of the test through a series of seasons. Such sources of error as those mentioned do not necessarily affect the variability of the yields of replicate plots, as Kiesselbach' has pointed out, and are therefore more likely to escape notice. They are systematic errors affecting the yields of replicate plots similarly. Marked superiority of Turkey wheat over Fulcaster in a variety test in Kansas does not indicate the superiority of Turkey over Fulcaster in Illinois, no matter how low plot variability in the variety test may be, because the growing conditions in Illinois are different from the growing conditions in Kansas. Similarly the superiority of Turkey wheat over Fulcaster in a rod-row test may not mean its superiority under field conditions in the same locality, because here again growing Experiments in Field Plot Technic 7 conditions are different. The error in applying the results, though of course much less in degree, is similar in kind. And, since the rod-row test has no purpose but to indicate the relative value of the strains tested, for field conditions, any pronounced tendency to favor some varieties at the expense of others is fatal to its object. Ordinarily, however, the rod-row test is only the first stage in variety testing, and final recommendations are based upon results of tests under conditions which approach those of field culture more closely. When the elimination of varieties in the rod-row tests is not extremely strict a considerable latitude may be allowed, and under these conditions the rod-row test has served a valuable purpose. It is of course desirable nevertheless to reduce these errors to the greatest possible extent. Probably the most important of the errors mentioned is that arising from the competition between different varieties, in the single-row test. Obviously a variety grown in a single row between two different va- rieties may yield considerably more or less than the same variety grown between two rows of its own kind. Various expedients for re- ducing varietal competition have been suggested. Sometimes the order of varieties is changed in each series to bring together different va- rieties and thus tend to equalize the effects of competition; sometimes an attempt is made to grow the varieties in such order as to bring together those of similar habit, and thus to reduce the effects of competition. Probably the most effective method is to grow border rows which may be discarded, and some investigators therefore use three-row or five-row blocks, in which the outer row on each side is discarded. The principal objection to the use of border rows in the increased area required to test the same number of strains, and the large pro- portion of the crop which is not harvested for yield. This is par- ticularly true when 3-row blocks are used, since in this case two- thirds of the field is used for border protection. The border rows may be us,ed for seed, but two-thirds of the field is of course much more than is required ordinarily for this purpose. When 5-row blocks are used the proportion of the crop harvested for yield is increased from one-third to three-fifths, though it is an increase in size of plot, with some decrease in replication, so that there may be no gain in accuracy. There is a possibility that the effect of competition on the yield of 5-row blocks may be slight enough to permit the harvesting of all five rows for yield, particularly if the varieties may be effectively arranged for the reduction of competition. At any rate, in such plots the error from competition may be expected to be much less than that in single- 8 Missouri Agr. Exp. Sta. Research Bulletin 49 row plots, since only two of the five rows are subject to competition with a different variety, and each of these is subject to such compe- tition on only one instead of on both sides. Another phase of the question which should not be overlooked is the effect of adding border rows on the error from soil variability. If, for example, each rod-row is to be protected from competition by two border rows, the test will require three times as large a field as the same test without the border rows. This can hardly fail to in- crease materially the variability of the yields of replicate plots, to an extent which will vary with the uniformity of the field concerned. The use of border rows may thus necessitate the use of an even greater number of replications for the same degree of accuracy, as far as plot variability is concerned. It is possible that 3-row plots (whether or not provided with border rows) may require less replications for a given degree of accuracy than single-row plots, on account of their larger size. It is possible also that 5-row plots, because of their size, may have an advantage over 3-row plots in reducing va- riability, great enough to justify in practice harvesting all five rows for yield, rather than harvesting the interior three rows and discarding the border rows. The importance of any practice that will reduce the variability of the replicate plots is thus increased when border rows are introduced. A familiar method for this purpose is the adjustment of yields by means of distributed check plots. In following this method the yields of check plots are considered measures of the productivity of the soil, which is usually assumed to vary uniformly between them. The yields of the experimental plots are adjusted on the basis of uniform productivity of the field as a whole. Of late this method has rather lost favor among agronomists. In some cases the adjustment actually increases rather than decreases the variability of the replicate ex- perimental plots. Check plots have not been used extensively in ad- justing yields in rod-row tests, principally because of the great in- crease in computation necessary in adjusting the yields of such a large number of plots. Experiments in Field Plot Technic 9 PLAN AND METHOD OF INVESTIGATION The experiments here reported were designed to obtain informa- tion on several factors affecting the accuracy of preHminary variety and strain tests, with a view to devising, if possible, an improved technic for this important phase of crop improvement work. The data obtained bear directly on the following points: 1. The extent of error from varietal competition in bor- der rows, and the relation of such competition to the charac- teristics of the varieties, 2. The relative variability of plots of 1, 3, and 5 rows, and the number of replications necessary for a given degree of precision with plots of the three sizes, and 3. The effect on variability of adjusting yields by means of check plots. Terminology. — In this report the term plot will be used to des- ignate an area on which a single variety or strain is grown, in com- parison with other varieties or strains, m other plots. The plot may consist of one or more rows. A plot of more than one row may also be referred to as a block. The single outside rows of the block are the border rows. A single-row plot protected from competition by border rows, which are to be discarded, will be spoken of as a protected single-row plot. A protected single-row plot is therefore a 3-row plot with border rows discarded, and a protected 3-row plot is a 5-row plot with border rows discarded. The phrase "3-row plots replicated five times" will be used to refer to 3-row plots in five systematically dis- tributed locations, not in six. The area on which a complete variety or strain test is conducted is spoken of as an experiment field, or simply a field. A group of plots including one plot of each variety or strain tested is a series. When four replications are used there are four series of plots. The group of contiguous plots from one side of the field to the other constitutes a range. The ranges are separated by alleys. Thus the field shown in figure 1 consists of sixteen ranges, each range including twenty-nine 5-row (or protected 3-row) plots. Ninety- six varieties were tested on this field, each replicated four times. Ranges I to IV, inclusive, make up the first series, V to VIII the sec- ond, IX to XII the third, and XIII to XVI the fourth. Each of the four strips running lengthwise of the field and separated by the check plots may also be considered a series. All yields are expressed in bushels per acre by weight, computed on the basis of 60 pounds per bushel for wheat, 48 pounds for barley, 10 Missouri Agr. Exp. Sta. Research Bulletin 49 B CH n 33 id 65 81 CH 21 37 S3 63 35 CH 2541 57 73 Cli 29 45 61 77 93 Cti B CK 18 34 SO 66 62 OK 22 38 54 70 86 CK 26 42 56 74 90 CHl4 30 46 62 73 94 CK B CH IS 35 SI 67 b3 CH 23 33 55 7/ 87 CK 274355 75 CH 15 31 47 63 79 95 Cli CK 20 36 S2 68 64 OH Z4 40 56 72 88 CHIZ Z8 44 60 76 92 CHl6 32 48 64 80 96 CH CH 21 37 53 69 85Ct{9 25*4! 57 73 83 CKia Z9 45 77 93 CH 17 33 49 65 81 CH B CH 22 3S 54 70 66 CH 10 26 42 58 74 90 CKI4 30 46 62 78 34 CH la 34 so 66 82 CH B CH 23 dB 55 67C/ill 27 fj 59 75 9/ CH IS 47 63 75 95 CH 19 35 SI 67 83 GK B CK^ 24 40 56 72 earn iz 28 44 60 76 92 CK 16 32 64 80 96 CH 20 35 52 68 64 CH Cl\ 25 41 57 73 CH 13 29 45 61 7793 CH I 17 33 49 65 81 CH 21 37 53 6985 CH B CHiO 26 i-2 56 74 30 CHI4 30 46 62 76 5f CH2 18 34 50 66 82 CH Z2 36 54 70 66 CH B CHli 2743 59 75 SI CH 15 31 47 63 79 95 a 3 19 35 51- 57 83 CH 23 39 55 71 87 CH B on 12 28 44 60 76 92 CH/6 32 46 64 80 96 CH zo 56 52 a4CHa 24 4C 56 72 66 CH BCHI3 29 45 61 77 33 CH 17 33 49 65 CHs 21 37 53 69 35 CH 25 41 57 73 89 CH B CHli do 46 62 78 94 CH IS 34 50 66 82 CH6 ZZ 38 5i 70 CH 10 26 nsa 74 90 CH CHI5 31 47 63 79 95CH 3 19 35 51 67 83 CH7 23 39 55 7/ 87 CH 27 43 \S9 75 91 CH B CHI6 32 48 64 0096 CH4- ZO 36 52 6864 CH3 24 40 56 72 CH 28 44 6Q 76 92 CH Figure 1.— Planting Plan of Wheat Variety Tests 1920 and 1921. Legend: B, border. CK, check. Numbers 1-96, planting numbers of varieties tested as given in Tables 4 and 5. Experime;nts in Field Plot Technic 11 and 32 pounds for oats. The measures of variability used are the average deviation, the standard deviation, and the probable error. These were computed according to the following formulae : in which A.D. = average deviation, o-==standard deviation, E = prob- able error (of a single determination), d == the deviation of a single variate from the mean, and n = the number of variates. The correla- tion coefficient r was determined by the formula \ n / \o-xo-y and the probable error of the correlation coefficient Er by the formula .6745 (1 — r^) E,= ±- Vn The tests reported are of two kinds, variety tests and strain tests. The variety tests were comparisons of commercial varieties, most of which were taxonomically distinct. A number of pure line selec- tions were included in the wheat variety tests. The strain tests were comparisons of a considerable number of commercial lots of the same variety obtained from different sources. These strains, so-called for convenience, are not, except in a very few cases, pure lines. Some of them are possibly identical, and all the strains of any one variety are of course very similar, since they are taxonomically the same. Procedure.— In the seasons of 1919, 1920, 1921, tests of va- rieties and strains of oats, barley, and wheat were conducted in blocks consisting of five rows ten inches apart and usually 18 feet long. From 24 to 96 varieties were included in each test, and from three to six (usually four) replications were used. The planting order in each case was designed on a plan similar to that illustrated in figure 1. It will be noted that the check plots were in continuous strips, that each variety was represented in each quarter of the field, whether divided from east to west or from north to south, and that in all four series each variety occupied the same position with relation to the check plots, and had the same varieties adjoining it on either side. 12 Missouri Agr. Exp. Sta. Research Bulletin 49 The rows in some cases ran east and west, and in some cases north and south. All these plots were seeded with a 5-row nursery drill, built from plans furnished by Professor T. A. Kiesselbach of the Nebraska Sta- tion. This is a hoe drill designed for rapid and thorough cleaning between plots. Photographs of it have been published in reports of earlier work on field plot technic at the Nebraska Station (Mont- gomery" page 57, and Kiesselbach " page 16). Its use resulted in uni- form seeding and covering and accurate spacing between rows, with a close approach to ordinary field conditions in the state in which the field was left after seeding. Each field was seeded in a single day. All plots were harvested by hand with sickles, a foot at each end of each row discarded, and the remainder (usually 16 feet) tied in a bundle and hung in a ventilated shed to dry. In 1919 and 1920 each row was bundled and threshed separately; in 1921 the border rows of each 5-row block were bundled separately and the three in- terior rows bundled together. Yields were determined by weighing in grams at the time of threshing. All final yields were converted to bushels per acre and are so expressed. Work of 1919. — In 1919 tests were conducted with barley and oats. Thirty varieties of barley were grown, each in 3 replicate plots. The test comprised three ranges of 185 rows each, including 21 check plots, or one in every sixth plot. The barley was drilled at the rate of eight pecks per acre, on March 21, in rows running north and south. The rows were 14 feet long and 10 inches apart. They were cut to 12 feet in harvesting. The planting plan is shown in figure 2. Conditions en CA Cl\ CK 20 CK SI 22232"} 25 CM 262128 2330 CK CKZI 23 24 25CI\26 27 2SZ9 30 on on a 13 14 O/i/6 19 ZO OH Ctill 0/116 17 18 20 22232425 CKZb 2728 23 dOGK CH6 CH Figure 2. — Planting Plan of Barley Variety Test 1919. Legend: B, border. CK, check. Numbers 1-30, planting numbers of varieties tested, as given in Table 1. were fairly favorable, and the yields of the adapted varieties were slightly higher than the average obtained under the conditions at Co- lumbia. Two varieties, Italian and Australian White, gave extremely low yields and were excluded. Another, Sandrel, was represented only in two series, and was also excluded. The yields of the remain- Experiments in Field Plot Technic 13 ing 27 varieties are shown in Table 1. The planting numbers given in this table correspond to those shown in the diagram of the field (figure 2.) Table l. — ^Yields of Barley Varieties. In Bushels per Acre. 1919. Planting Average Yield number Variety 3 interior rows 5 rows 1 Hanna 906 12.55 12.57 2 Steigum 907 19.90 19.65 3 Luth 908 23.65 23.40 4 Eagle 913 20.40 20.13 5 Italian 914* 6.70 6.57 6 Servian 915 19.85 19.86 7 Odessa 916 13.75 13.41 8 Lion 923 21.75 22.14 9 Australian White 925* 1.45 1.74 10 Horn 926 21.25 21.54 11 Odessa 927 20.80 19.53 12 Summit 929 23.05 24.03 13 Mariout 932 18.75 18.15 14 Odessa 934 10.30 9.84 15 Peruvian 935 22.25 20.55 16 Trebi 936 30.90 30.96 17 Sandrel 937* 35.90 33.48 18 Oderbrucker 940 23.35 23.79 19 Prankish 953 22.50 22.05 20 Manchuria 956 30.80 30.03 21 Oderbrucker 957 29.45 29.52 22 Manchuria x Champion of Vermont 959 18.30 17.49 23 Luth 972 25.05 26.28 24 Red River 973 27.25 28.14 25 Featherston 1118 28.25 27.00 26 Featherston 1119 25.80 25.83 27 Featherston 1120 34.35 35.49 28 Hanna x Champion of Vermont 1121 13.75 13.92 29 Manchuria 1125 20.35 20.94 30 Malting 1129 17.25 16.44 Mean 22.06 21.95 Forty varieties of oats were compared in 1919, but only 24 of these could be replicated 4 times and the remaining 16 were duplicated. The planting plan was therefore arranged as for 32 varieties, and these 16 varieties grown in two plots each in place of eight varieties *Italian 914 and Australian White 925 were omitted from all computations because of their extremely low yields, and Sandrel 937 because omitted in the third series. 14 Missouri Agr. Exp. Sta. Research Bulletin 49 a 1 2 3 4 — 5 6 7 a CK 9 10 II 12 13 14 IS 16 Ch 17 la f9 20 Zl ZZ 23 24 CK 85 Z6 27 Z6 Z330 31 3Z CHB CK S3 yt J3 36 37 38 39 w CH 1 2 3 4 5 6 7 a Ch 9 10 II 12 13 14 15 16 Ch 17 IS 19 2021 22 23 24 CK B CK 17 18 13 20 21 Z2 23 24 J Z5 26 27 28 29 30 31 32 CK 1 2 3 4 5 6 7 8 en 9 10 II 12 13 M 15 16 ChB CK 3 10 II IB 13 /4 15 16 OH 17 18 19 20 21 22 2d 54 CK 33 34 35 36 37 38 39 4CCH 1 2 3 4- S 6 7 6 CHB en 5 £■ E D M U L T 1 P L 1 C /? T 1 N ChB Ch 1 2 3 f S Ch 6 7 8 9 10 Ch II 12 13 14 15 CK / 2 3 f 5 Ch 6 7 8 9 /O Ch II 12 13 /f 15 Chb CH II 18 13 14 15 CK 1 S 3 f 5 Ch 6 7 a 9 10 C/i II 12 13 14 15 CH 1 2 3 f 5 Ch 6 X X 9 lOCHB " 6 7 8 9 /OC/f II IS 13 If 15 Ch 1 Z •3 1 f 5 C/l 6 7 6 9 10 CH// 12 13 li 15 Ch X 2 X X CHB Figure 3. — Planting Plan op Oats Variety and Strain Tests 1919. Legend: B, border. CK, check. Numbers 1-40 in first four ranges, planting numbers of oats varieties, as given in Table 2. Numbers 1-15 in last three ranges, planting numbers of oats strains, as given in Table 3. X, test plots planted to check variety because of insufficient supply of seed. Table 2. — Yields of Oats Varieties. In Bushels per Acre. 1919. Planting Average yield in interior rows number Variety Four series Three series 1 A. Sterilis nigra 30.0 31.7 2 Black Mesdag 44.2 44.7 3 C. I. 602 35.4 38.1 4 C. I. 603 53.9 55.1 5 C. I. 620 13.1 14.1 6 Early Champion 55.5 53.9 7 Early Gothland 54.1 52.8 8 Carton 473 30.6 31.7 9 Carton 585 21.7 23.0 10 Colden Ciant 42.0 44.9 11 Irish Victor 69.6 70.2 12 Japan Selection 47.9 50.9 13 June 43.1 44.5 14 Kherson Selection 67.2 63.1 15 Fulghum 042 60.9 57.1 16 Lincoln 51.5 50.3 17 Monarch 56.0 53.4 18 North Finnish 51.0 49.5 19 Scottish Chief 59.3 60.1 20 Sparrow bill (Missouri) 39.8 41.3 21 Sparrow bill (Cornell) 42.3 45.7 22 Tobolsk 1 52.6 57.3 23 Tobolsk 2 46.1 51.9 24 White Tartar 49.7 50.3 Mean 46.6 47.3 EXPEIRIMENTS IN FlELD PlOT TeCHNIC 15 in four plots each, as shown in figure 3. The rows were 14 feet long and were cut to 12 feet in harvesting. This is a convenient size of plot for oats tests with 10 inches distance between rows, when the border rows are discarded, since the total yield of three rows in grams, divided by 10, gives the yield in bushels per acre. The oats were planted at the rate of 10 pecks per acre, on March 18, in rows running north and south. The season was favorable and a good yield of the better varieties was obtained. The yields of the 24 varieties replicated four times are shown in Table 2. The oats strain test was conducted on the same field, as shown in figure 3, directly south of the oats variety test. In planting, these two tests were handled as one ; and the rate, date, and method of planting were the same. The strains tested were 15 strains of oats obtained •under the name Red Rustproof from various experiment stations and seedsmen. Three of these strains, 0121, 0124, and 0127, were not true to name, but the remainder were taxonomically Red Rustproof oats, as described by Etheridge^ The oats strains were tested in six series, with check plots in every sixth plot. The line of check plots on the west, however, gave abnormally low yields, probably because they were located partly on a dead furrow at the edge of the experiment field. On account of shortage of seed some of the varieties could not be planted in the last series. The first and last series were therefore dis- Table 3. — Yields of Oats Strains (Red Rustproof). In Bushels per Acre. 1919. Planting Accession Average yield number number 3 interior Rows 5 Rows 1 0119 2 0120 3 0121* 4 0123 5 0123 6 0125 7 0126 8 0127* 9 0124* 10 0133 11 0128 12 0129 13 0130 14 0131 15 0132 Mean 49.58 49.41 45.83 44.51 49.43 53.01 47.85 49.59 53.55 53.47 50.18 49.19 44.85 45.81 38.55 36,67 63.90 67.46 48.00 46.49 53.55 53.15 49.35 49.01 52.73 51.89 48.60 47.84 55.13 55.44 50.07 50.20 *Not taxonomically Red Rustproof. 16 Missouri Agr. Exp. Sta. Research Bulletin 49 carded. The average yields of the 15 strains in the four remaining series are shown in Table 3. Work of 1920. — ^Wheat varieties were grown in 5-row blocks in 1919-20. Ninety-six varieties were included in the test, four replica- tions being used. Fultz wheat was grown as a check in every sixth plot. The rows were 18 feet long and were cut to 16 feet in harvest- ing. The direction of the rows was east and west. The planting plan is shown in figure 1. The wheat was sown October 15, at the rate of 6 pecks per acre. There was considerable winter injury in the plots and the condition of the wheat in early spring was rather poor. The yields obtained are shown in Table 4. Table 4. — Yields of Wheat Varieties. In Bushels per Acre 1920. Average yield Planting 3 Interior 5 number Variety Rows Rows 1 Beechwood Hybrid No. 12.. 10.8 11.1 2 Beechwood Hybrid No. 81.. 12.8 14.1 3 Beechwood Hybrid No. 85.. 12.5 12.7 4 Beechwood Hybrid No. 87.. 14.2 13.7 5 Beechwood Hybrid No. 202. 11.9 12.S 6 Beechwood Hybrid No. 207. 13.2 13.6 7 C. I. 3808 16.2 16.6 8 C. I. 3846 14.2 15.6 9 C. I. 3972 14.7 15.6 10 C. I. 3980 16.4 17.5 lie. I. 3988 16.7 17.0 12 C. I. 4004 14.3 14.0 13 Common Rye 17.3 18.5 14 Dawson's Golden ChaiT 13.0 12.3 15 Deitz 15.1 14.6 16 Early Ripe 12.2 12.6 17 Early Ripe No. 26 13.2 14.0 18 Early Red Clawson 9.9 9.5 19 Farmer's Friend 18.8 19.9 20 Fulcaster 14.4 15.3 21 Fultz (Archias) 12.2 13.0 22 Gold Coin 11.7 12.2 23 Greene County 15.6 15.1 24 Harvest King No. 7 13.4 14.2 25 Harvest Queen 9.6 9.8 26 Hicicman ?.8 812 27 mini Chief 17.5 18.7 28 Jones Climax 19.1 20.7 29 Kanred 21.0 22.7 30 Kessinger 18.0 19.3 31 Kharkov 18.9 20.1 32 Leap's Prolific 14.2 14.8 33 Mediterranean No. 8 9.1 9.5 34 Michigan Amber 10.7 11.3 35 Michigan Amber (Indiana) 17.0 17.9 36 Michigan Amber No. 7 ... 10.5 10.8 37 Michigan Amber No. 12 . . . 9.3 9.3 38 Michigan Wonder 10.9 11.1 39 Michigan Wonder No. 4 ... 12.4 12.7 40 Michigan Wonder No. 8 ... 10.8 11.0 41 Michigan Wonder No. 21 . . 8.2 8.7 42 Michigan Wonder No. 53 . . 8.5 9.6 43 Michigan Wonder No. 54 .. 11.3 10.7 44 Michigan Wonder No. 83 . . 13.6 13.7 45 Michigan Wonder No. 96 . . 9.7 9.7 46 Michigan Wonder No. 103 . 9.7 9.1 47 Michigan Wonder No. 116 . 16.4 15.8 48 Michigan Wonder No. 130 . 14.3 14.2 49 Michigan Wonder No. 140 . 12.3 12.7 Average yield Planting 3 Interior 5 number Variety Rows Rows 50 Michigan Wonder No. 141 . 10.7 10.3 51 Michigan Wonder No. 155 . 10.1 9.8 52 Michigan Wonder No. 209 . 12.1 12.5 53 Michigan Wonder No. 211 . 9.9 9.9 54 Michigan Wonder No. 221 . 11.0 11.1 55 New York 123-32 17.2 17.5 56 Niagara 13.8 13.5 57 Nigger 11.8 11.8 58 Old Ironclad 12.5 13.2 59 Poole 10.5 10.7 60 Poole No. 3 11.7 11.0 61 Poole B-3 12.5 13.3 62 Portage 15.9 17.3 63 Pride of Indiana 14.2 14.4 64 Pride of Genessee 15.7 18.1 65 Reliable 12.6 12.9 66 Red Cross 13.1 13.1 67 Red May i4.8 14.8 68 Red Rock (Indiana) 18.7 19.7 69 Red Rock (Michigan) 7.5 6.8 70 Red Wave 12.9 12.7 71 Rochester Red 12.7 12.9 72 Rosen Rye 20.7 24.0 73 S. P. I. 11616 10.3 10.9 74 S. P. I. 26012 13.4 12.9 75 S. P. I. 26013 15.2 15.5 76 S. P. I. 26014 17.5 18.8 77 S. P. I, 26015 13.2 13.4 78 S. P. I. 26017 13.4 13.5 79 S. P. I. 26018 13.6 13.6 SOS. P. I. 26019 11.6 11.6 81 S. P. I. 26022 10.6 10.1 82 S. P. I. 26023 9.1 8.5 83 S. P. I. 26025 12.3 13.1 84 S. P. I. 26029 15.4 15.6 SS S. P. I. 26085 13.2 13.3 86 Treadwell 12.7 12.8 87 Valley 12.4 12.1 88 Velvet Chaff No. 2 14.1 12.8 89 Velvet Chaff No. 8 9.0 9.3 90 Ziegler's Fly Proof 10.9 11.7 91 13U-4a 14.1 13.9 92 37a-4 14.6 14.7 93 Fulcaster (Co-op) 17.4 18.5 94 Fultz (Co-op) 15.2 15.9 95 Kanred (Co-op) 19.1 20.6 96 Poole (Co-op) 19.4 21.0 Mean 13.4 13.8 Experiments in Field Plot Technic 17 0) O o CO <« r/i <.S2 5.2 CL,:?; 4> o »» m O ■<.Si ^ 5 i' 0.2 f"" lU to C ^ .S o ir)^OTtro\0»--'^HfOv^O\0\caOO.2^0CM ( CvjIM-a CM I .000^0'^CMfO'*>/1^t^OOO\0-H(NlcO'*>/1VOI--.000\0 ^., tSCVI tn O O o ?H O S 3 S 3 « u «.*; OoOw^M M-*TtO\(Nl'HOCOinOO\UlM©ThOOOOOOCOrH'*OsO\C]rHM tv;oN-Hdr-;codinuit^iXvoo\0\Wcr\o6-oodTr^'co^rov2coiXco-^ CTicovovo-^iovo-o-iooo ooooootTvt^uiinoo rt ^ ^ ^ rt (M r-( .-H -< ^ -1 'H rH ,-, rt ,-( rH rH rt ■-! ,-1 rt rH rt rt T-< ^ .-1 i-Hi-l ,1 ^ rt r-1 rH i-l f-1 i-C r-1 rH ,-1 f-l >-l i-H ,-1 rH .1 v0^ot^r^OMcot^Tf(^^»o<3\.-l^A■*^oot^oo\qoocslqq<^lco>o^^.«OT^^..<»^-.u^^X)ClOln^^ r^ddd^'co\drfTfioinuio\odc)6c»o6>Xvdiot>^uidcovdcoTr o\'*^io'*"^t^^'"f^'~»'^'^2^ 2i"^^ <»T^T^oOlnT^looo-HVOT^(^5lnI^ot^^^co^»I^o^rt"^oooo<^l^^co^o•*Mu^(^^^o>nt^lr)^o^^eo vod-^-^^■codu^lr>|v;u^^no^a3o6o\t>;■^'^>.'>nc6u^c^^co^oco^>.'■^>-^coT)■■d t^^>.O^M^C.-^Ol»0^^0^0■*MOO^wcoOa^OOOl^l.-HMu^.-^coCSlO^^. ONONin'-ivOqvOOv^^ ^odd--.-^''0^-;*'Tf■vdlnVo^oo^..■od^^u^t^u^odr^McoT^co'^■;T^^co■*dT^■^oy3■*l^ ^ '-^i w VOM ^co Ol • J^ogrt VO O too "1 MM /^ 0) ^, U ••^■-ii. V, h V. I, I. 1- I- i-r)P50u xir; a 4) Pifi:;p:J (fl (u i! u S iJ 4; ij «^C--_-si*jjjU ^^ o d'-' o o o" o' d d d d d V tu V V V aji>o •^^^•^ CggCCflCCCO uC cSceSo^^oooo OOO i!^.^2SCC33'=Cf^3CBC3CC e O u ubjJbobobBbobpby bo M_5f hf bo bo bp :6^o ovujJJJi^*^;^*i^c^ a G m rt ^^ "p "o "S "S "S "S "S "o "5 "o "o "o "5 "S "S . o— " « « rt m'3,?'3'3 3 3 3 3 3 3 3 3«2 Oi'5.'3k>::^ '^*S»S^i5i5'5*5'5'5'5SSSSSS wucJuuuc rtMCOT^lnvOt^OOO^OrtMcoM-^r)VOt^(»C^OrtMc^T^lO^O^^OOa^O^M'25vOVOt>.C03^0rHM^2:!S5C;2^ VN '-I '^'^'~"'^^^„^^^^^„f,q5y,l>j(Sl(Sl(sj{>qCNlMC« s's t " " o § 27 2L30 24 27.67 15 13.11 94 19.79 94 18.85 30 14.28 32 39.15 Date of Heading. Coefficient of Correlation between Competition and — Date of Maturity. Grain- Straw Ratio. Height. Yield. Barley variety Oats variety Oats strain Wheat variety Wheat variety Wheat mixture Oats variety 1919 1919 1919 1920 1921 1921 1921 -.153 + .120 — .376±.136 — .5i5±.048 — .271±.060 — .514±.083 — .648+. 060 .063±.123 .456±.103 .244±.157 .552±.045 .222±.062 .613±.070 .860+. 028 + .072±.122 — .091 + .129 + .012±.159 + .347±.057 + .442±.099 +.314±.117 + .316±.143 + .582±.043 + .294±.059 + .S54±.078 +.484±.082 tion to competition in every case, the results of the tests are fairly consistent. The correlation of competition with yield is always posi- tive, and is fairly high in every case, the lowest coefficient being -|-.294 ±.059. From these results there can be no doubt that the higher yield- ing varieties are those which in general have profited by competition. The date of heading and the date of maturity show a negative correla- 42 Missouri Agr. Exp. Sta. Research Bulletin 49 tion with competition in each case, though some of the coefficients are insignificant. It is clear therefore that early varieties are, in gen- eral, able to compete more strongly, but the extent of this relation is quite variable. The grain-straw ratio showed no significant relation to competition in any of the experiments of 1919, and was not deter- mined for the succeeding tests. Height was correlated positively with competition in the one test in which height was determined, the wheat variety test of 1921. In this test height was more closely related to competition than were date of heading, date of maturity, or yield. In the oats variety tests, the relation of early maturity to compe- tion is particularly marked, the coefficients of correlation in both oats variety tests being distinctly greater for date of maturity and compe- tition than for yield and competition. In the wheat tests there was little difference in the degree of relation to competition between earli- ness and yield. In the one test of barley varieties conducted, yield was more closely correlated with competition than was either the date of heading or date of maturity, but none of the three showed a clearly significant correlation. It is clear that in these trials the early, high-yielding varieties profited by competition. To a considerable extent these may be the same varieties, for the correlation of earliness and yield was high in most of the tests conducted. The relation of earliness and other characters to yield under Missouri conditions will be considered more fully in another paper, but data of interest in this connection are ap- propriate here. The coefficients of correlation of yield with date of heading and date of maturity in the variety tests discussed in this paper are shown in Table 18. Table 18. — CoRREivATioN OP Yield With Dates op Heading and Maturity in Variety Tests of Barley, Oats, and Wheat Number of Crop Season varieties Coefficient of correlation of yield with — Date of heading Date of maturity Barley 1919 27 Oats 1919 40 Oats 1921 32 Wheat 1920 94 Wheat 1921 94 -.281 ±.120 -.750 ±.052 -.511 ±.051 -.331 -+-.062 — .271 ±.120 —.627 ±.065 — .894 ±.024 — .642 ±.041 — .419 ±.057 When a very high correlation exists between earliness and yield it is likely that a character closely correlated with one may show a high degree of correlation with the other, which might not be shown were it not for the first correlation. For example, suppose earliness Experiments in Field Plot Technic 43 of maturity is largely responsible for strong competitive value. Then in a season when earliness is closely correlated with yield a close cor- relation of competition and yield is likely to be found, not because high yield makes for strong competition but because the high-yielding va- rieties are early. Conversely, the competing value may be dependent on the yield and the correlation with earliness may be incidental, under the same conditions. If the relation of earliness and yield were con- stant, such a question would have little practical importance, but when the relation is reversed, as it may be in different localities and even in different seasons in the same locality, the relation of competition to the two characteristics may be very different. The relation of compe- tition to earliness and yield in these tests, therefore, may be due pri- marily to the predominating influence of either of these two charac- teristics, or to the influence of both. General conclusions regarding competition should not be drawn from these tests. The problem of competition is complicated by many factors, and will require numerous and extensive investigations for its solution. These results, however, indicate that gross errors from this source are commonly involved in variety tests, that such errors occur both in rows running east and west and in rows running north and south, that the error is less when the varieties and strains com- pared are structurally similar than when they are widely different, and that the error may be reducible to some extent by the grouping of va- rieties according to the time of maturity and possibly other characters, when the relation of such characters to competition is more fully studied. In the present state of knowledge regarding the relation of competition to the characteristics of the varieties compared, the use of border rows is highly desirable, since by their use the error from competition can be practically eliminated. SIZE AND REPLICATION OF PLOTS. Previous Investig-ation. — Most of the direct evidence reported on replication and size of plots has been obtained in experiments in which a field of a uniformly handled crop is harvested in a large num- ber of small sections. These sections are grouped to form plots of different shapes and sizes, and systematically distributed sections are averaged to represent replicate plots. The relative variability of the yields determined by each plot arrangement is the criterion of expe- rimental accuracy. Such experiments have been reported by Morgan" with wheat and fodder corn. Wood and Stratton" with mangels, Mer- cer and Hall " with wheat and mangels, Hall and Rusself with wheat, 44 Missouri Agr. Exp. Sta. Re;se;arch Bulletin 49 Montgomery"'" with wheat, Kiesselbach" with oats, and Day^ with wheat. The general conclusions drawn from these experiments are in harmony, though the specific size and shape of plot and number of replications found most desirable vary rather widely. In general, plot variabilit}' was reduced by increasing the size of the individual plot, up to a certain limit, but it was reduced much more effectively by rep- lication of plots. For a given area a large number of small plots was always found more accurate than a small number of large plots. But the size of the plot cannot be reduced indefinitely for several reasons. As the plot becomes smaller the proportion subject to "bor- der effect" rapidly becomes greater. This border effect may be due to the modified growth of plants adjoining an alley or to the in- fluence of the competition of different varieties in adjacent rows. If the borders are not discarded an important systematic error is involved ; if they are discarded a considerable portion of the land and labor is lost. In either case the disadvantage is increased as the size of the plot is decreased. When single rod-row plots are used the whole plot is subject to border effect. .The importance of this error has already been discussed. Another disadvantage of the extremely small plot is that slight differences in stand and small mechanical er- rors have a marked effect on the yields. The increased labor involved in handling a large number of small plots rather than a small number of large plots is also an important disadvantage. The length of the so-called rod-row has usually been determined by convenience. Commonly used lengths when the rows are a foot apart are 16 feet for wheat, 20 feet for barley, and 15 feet for oats, since with these lengths yields in grams per row may easily be con- verted to bushels per acre. In other cases the most convenient length is determined by the dimensions of experiment fields. Although in- creasing the length of the row would doubtless reduce variability, a greater gain could be made on the same area by further replication. Ordinarily it is preferable, therefore, to retain the most convenient length and to make any desired increase in size of plot in the width, for widening the plots will rapidly reduce the proportion subject to border effect. Experimental Results. —Size of Plots. — By comparing the stand- ard deviations of single rows and blocks consisting of three and five rows each, in the check plots, it is possible to determine the relative value of plots of the three sizes in counteracting plot variability. In this comparison the single-row and three-row plots correspond respec- tively to 3-row and 5-row plots in which the border rows are dis- Experiments in Field Plot Technic 45 carded, since they are made up of rows protected from varietal compe- tition by border rows. In each of the computations summarized be- low each check plot is represented by only one yield. For example, in determining the yield and standard deviation of single rows in the 20 check plots of the oats variety test of 1919, the constants for single rows are the average of determinations made independently for Row 2 of each of the 20 plots, for Row 3, and for Row 4. The determina- tions for 3-row plots are similarly made from the computed yields of the three interior rows of each check plot, and those for 5-row plots from the computed yields of the entire plots. Thus each determination represents the same number of plots and the same area, the only dif- ference being in the size of the individual plot. It would be possible, of course, to test 40 per cent more varieties with the same number of replications or to increase the number of replications by 40 per cent for the same number of varieties on the same area, if 3-row blocks were used rather than 5-row blocks. The yield and variability of check plots of different sizes in the barley variety test of 1919 are shown in Table 19. The variety grown in these check plots was Oderbrucker, seeded at the rate of 8 pecks per acre. The check variety was grown in every sixth plot. Table 19. — Yield and Variability of Check Plots. Single-row, Three-row, and Five-row — Barley Variety Test 1919. Number Yield Size of plot of plots per acre Standard deviation bu. bu. % Single-row Row 1 21 41.26 7.95 19.26 Row 2 21 36.71 8.30 22.61 Row 3 21 37.15 8.48 22.84 Row 4 21 35.82 10.37 28.96 Row 5 21 42.12 11.86 28.16 Alean of three interior rows 21 36.56 9.05 24.80 Mean of five rows 21 38.61 9.39 24.37 Three-row Plot (Interior rows) 21 36.56 8.11 22.18 Five-row Plot 21 38.61 8.29 21.47 The variability of the single-row plots is 12 per cent higher on the average than that of the 3-row plots. That is, 3-row plots with 46 Missouri Agr. Exp. Sta, Research Bulletin 49 borders discarded would have given in this case somewhat more va- riable results than 5-row blocks with borders discarded. The same 5- row blocks harvested entire (with borders retained) gave slightly less variable yields than when the borders were discarded. The same comparison may be made in the check plots of the oats variety test of 1919. The check variety was Red Rustproof, drilled at the rate of 10 pecks per acre in every ninth plot. The re- sults are shown in Table 20. TabIvE 20. — Yield and Variability of Check Plots. Single-row, Three-row, and Five-row — Oats Variety Test 1919. Number Yield Size of plot of plots per acre Standard deviation Single-row Row 1 20 bu. 44.64 bu. 10.37 23.23 Row 2 20 47.97 9.81 20.45 Row 3 20 46.56 11.42 24.53 Row 4 20 46.95 13.81 29.41 Row 5 Mean of three 20 42.09 11.58 27.51 interior rows 20 47.16 11.68 24.80 Mean of five rows 20 45.64 11.40 25.03 Three-row Plot (Interior rows) Five-row Plot 20 20 47.16 45.64 10.62 9.72 22.59 21.30 The results in this case are practically identical with those of the barley variety test. Protected single rows were 10 per cent more va- riable than protected 3-row blocks, while the latter were only 6 per cent more variable than unprotected 5-row blocks. In the test of strains of Red Rustproof oats, conducted on the same field in 1919, adjoining the oats variety test, the same variety was used as check, and the crop was seeded on the same day with the same machine, but the check plots were in every sixth instead of every ninth plot. The corresponding data for these check plots are given in Table 21. Although the variability of these plots is lower, the relative va- riability of plots of different sizes is similar to that of the variety test. The single interior rows are on the average 24 per cent more variable than the 3-row block. The 3-row plot is only very slightly more va- riable than the 5-row plot. Experiments in Field Plot Technic 47 Table 31. — Yield and Variability oe Check Plots. Single-row, Three-row, and Five-row. — Oats Strain Test 1919. Number Yield Size of plot of plots per acre Standard deviation bu. bu. % Single-row Row 1 18 41.87 6.35 15.15 Row 2 18 40.88 5.52 13.51 Row 3 18 43.50 5.81 13.37 Row 4 18 45.00 7.31 16.25 Row 5 18 41.50 6.37 15.35 Mean of three interior rows 18 43.13 6.21 14.38 Mean of five rows • 18 42.55 6.27 14.73 Three-row Plot (Interior rows) 18 43.13 5.04 11.68 Five-row Plot 18 42.55 4.86 11.41 In the wheat variety test of 1920 the check variety was Fultz, which was seeded at the rate of six pecks per acre in every seventh plot. The results of interest in this connection are shown in Table 22. Table 22. — Yield and Variability of Checks Plots. Single-row, Three-row, and Five-row. — Wheat Variety Test 1920 Number Yield Size of plot of plots per acre Standard deviation bu. bu. % Single-row Row 1 80 20.74 6.58 31.72 Row 2 80 17.28 5.03 39.05 Row 3 80 18.34 4.50 24.53 Row 4 80 17.29 5.10 39.48 Row 5 80 19.37 6.00 30.97 Mean of three interior rows 80 17.64 4.87 37.68 Mean of five rows 80 18.60 5.44 39.15 Three-row Plot (Interior rows) 80 17.64 4.43 35.11 Five-row Plot 80 18.63 4.77 35.60 48 Missouri Agr. Exp. Sta. Research Bulletin 49 Again the single rows are distinctly more variable than the 3-row plot, in this case to the extent of 10 per cent. The 5-row and the 3-row plots are about equally variable, the slight advantage in this case being in favor of the latter. To summarize, it is evident that the protected 3-row plot is some- what less subject to plot variability than the protected single-row, but the relative value of the 5-row plot harvested entire and the same plot harvested as a protected 3-row block is not clear. Some further comparison of these two methods was made in 1921. The variability of the check plots in both the wheat and oats tests was computed as protected 3-row and as unprotected 5-row plots. In the wheat tests the check variety was Poole, seeded at 5 pecks per acre in every seventh plot in the variety test, and in every sixth plot in the mixture test. In the oats tests the check variety was Kherson, seeded at 10 pecks per acre in every sixth plot. The results are shown in Table 23. Table 23. — Yield and Variability of Check Plots. Three-row and Five-row. — Wheat and Oats Tests, 1921. Number Yield Size of plot of plots per acre Standard deviation bu. bu. % Wheat Variety Test Three-row Plots 80 14.89 2.16 14.50 (Interior rows) Five-row Plots 80 13.98 1.90 13.61 Wheat Mixture Test Three-row Plots 30 15.48 3.25 20.98 (Interior rows) Five-row Plots 30 15.78 3.55 22.49 Oats Variety and Strain Tests Three-row Plots 120 37.95 4.61 12.15 (Interior rows) Five-row Plots 120 38.37 4.70 12.25 In no case are the differences very great. The variability of 3-row blocks is slightly greater in the mixture test and that of 5-row blocks in the variety test of wheat. There is practically no difference between the two in the oats tests. Apparently there is no constant material gain in plot uniformity obtained by the inclusion of the border rows of the 5-row plot, even though the size of the plot is materially increased by this procedure. Even if variability were decreased by their inclusion, the practice would be of doubtful value in most tests, for the reasons given in the last section ; but with practically no decrease in variability there is left no Experiments in Field Plot Technic 49 reason for the harvesting of these rows. They are not wasted because they are not harvested, for they serve a valuable purpose; the waste would be involved rather in harvesting them, for the added labor and expense would contribute nothing to the accuracy of the experiment. Although protected 3-row plots are less variable than protected single-row plots, they are not necessarily preferable. Three protected 3-row plots require the same area as five protected single-row plots, and the harvesting of almost twice as large a crop (nine rows in the first case for every five in the second). If the mean yield of five single rows has as low a probable error as the mean yield of three 3-row plots, the protected single-row plot will ordinarily be pre- ferable, because of the reduction of labor in harvesting and thresh- ing. When the standard deviation of the check plot yields is known, the probable error of the mean of any number of replicate plots can be computed and the number of replications for any given degree of accuracy determined. If single-row plots were 29 per cent more variable than 3-row plots, the probable errors of the mean of three 3-row plots and of five single-row plots would be equal, since the prob- able error of the mean is equal to the probable error of a single deter- mination divided by the square root of the number of determinations, and since the square root of 5 is 29 per cent greater than the square root of 3.' In the cases herein cited the advantage of the 3-row plots was considerably less than 29 per cent in every case, and we may con- fidently expect therefore that protected single-row plots repeated five times will be less variable than protected three-row plots repeated three times, which would require the same area and more labor. Some further evidence on the relative variability of the protected 3-row plot and the unprotected 5-row plot, or, in other words, of 5-row plots, harvested with and without their border rows, may be ob- tained from the yields of the tested varieties and strains. Since the number of replications of each strain is small, average deviations are given instead of standard deviations. The inclusion of border rows in the 5-row plots should not increase variability, since the adjacent va- rieties are the same in each series, and the competitive effect should be no more variable than would be that of the same variety. A clear-cut comparison of 5-row and 3-row plots is therfore available in this case. In the case of the check plots this comparison was somewhat obscured by the competitive effect of different varieties on the border rows, which might be expected to increase variability and thus to conceal a possible advantage of the 5-row plot. The average variability of 3-row and 5-row plots in the strains tested in these experiments is shown in Table 24. In each case the 50 Missouri Agr. Exp, Sta. Resijarch Bulletin 49 figur,e given is the mean of the average variabilities determined for all of the varieties or strains in the experiment. Table 24.- YiELD AND Variability of Test Plots. Three-row and Five-row. Season Number of vari- eties Ntmiber of Repli- cations Three-row Plots Five-row Plots Test Yield bu. per acre Average Devia- tion % Yield bu. per acre Aver- age Devia- tion % Barley varieties 1919 27 3 22.06 15.35 21.95 15.44 Oats strains 1919 15 4 50.07 5.96 50.20 5.10 Wheat varieties 1920 96 4 13.39 24.27 13.78 24.36 Wheat varieties 1921 96 4 15.42 10.30 15.57 9.74 Wheat mixtures 1921 30 4 17.62 9.84 18.15 10.03 Oats varieties 1921 32 4 29.85 10.86 30.70 10.14 Oats strains 1921 64 4 28.40 10.82 28.63 10.58 There is no consistent difference in variability between the 3-row plots and the 5-row plots. In some cases the former are more va- riable ; in others the latter ; and in no case is the difference in varia- bility great. These results are contrary to the general impression that variability decreases with increase in size of plots. Apparently, in tests of this kind, the 3-row plot is lai'^ge enough to give a fair sample and nothing is gained by adding the other two rows. When it is con- sidered that th.e addition of these two rows undoubtedly introduces systematic error from competition to a greater or less extent, and involves a very considerable increase in the labor of harvesting and threshing, there remains little doubt that the border rows of 5-row plots are best discarded in .experiments of this sort. Replication of Plots. — It is generally considered that the error from soil variability may be reduced to any desired point by replica- tion in sufficient degree. For any given degree of precision the num- ber of replications required is dependent on the variability of the replicate plots. When every plot in a single-row test is provided with two border rows the area required for the test is tripled, the replicate plots are separated more widely, and variability is usually increased, since the range of soil variability will usually be greater when a larger area is included. The removal of border effect from the rows harvested for yield may in some cases reduce variability more than enough to balance this increase, but when the unprotected single rows are grown in the same order in each series, variability will not be much affected by competi- tion, as before stated. Consequently more replications of single-row Expe;riments in Fiei^d Plot Te;chnic 51 plots protected by borders than of the single-row plots not so pro- tected may actually be required for a given degree of plot variability. Similarly, more replications may be required in a test of a large num- ber of strains than in a test of a small number, as Montgomery" has suggested. The number of replications required may be determined with a fair degree of accuracy from the variability of the check plots. The variability of the check plots in parts of the large fields used as com- pared with the variability of the check plots in the whole fields shows the importance of this point. In Table 25 are given the standard de- Table 25. — Relation of Plot Variability to Size of Experiment Field. Check Plots in Wheat Variety Test 1920. No. of Size of field Plots Yield Standard deviation bu. per acre bu. % Four ranges (1st)* 20 14.79 3.789 25.62 Four ranges (2nd) 20 18.35 4.073 22.20 Four ranges (3rd) 20 16.67 3.659 21.94 Four ranges (4th) 20 20.74 3.876 18.69 Mean 20 17.64 3.849 22.11 Eight ranges (1st) 40 16.57 4.316 26.05 Eight ranges (2nd) 40 18.71 4.285 22.90 Mean 40 17.64 4.302 24.48 Sixteen ranges 80 17.64 4.430 25.11 *The four-range and eight-range sections are in order from west to east. viations of the yields of the check plots in the wheat variety test of 1920. The yields of the three interior rows of the check plots were used in computing these constants. Twenty-four varieties could have been replicated four times in the four ranges comprising any quarter of the field. As the probable error of a single plot yield is 14.92 per cent we may conclude that the probable error of the mean of four such yields would be about 7.46 per cent. But when 96 varieties must be tested, as they were in this test, four replications require 16 ranges, and the probable error of the mean yield becomes 8.47 per cent. A degree of precision which could be attained with four replications in a test covering four ranges could hardly be attained with five replications in a test covering sixteen ranges. Corresponding data for the wheat variety test of 1921 are given in Table 26. Although the variability in this experiment was much lower, the relative variability of large and small experiment fields was 52 Missouri Agr. Exp. Sta. Research Bulletin 49 Table 26. — Relation of Plot Variability to Size of Experiment Field. Check Plots in Wheat Variety Test 1921. Size of field Four ranges (1st)* Four ranges (2nd) Four ranges (3rd) Rour ranges (4th) Mean Eight ranges (1st) Eight ranges (2nd) Mean Sixteen ranges No. of Plots Yield bu. per acre Standard Deviation bu. % 16 16 16 16 16 32^ 33' 32 64 15.78 15.48 15.28 13.01 14.89 15.63 14.14 14.89 14.89 1.584 10.04 1.586 10.25 2.099 13.74 2.091 16.07 1.840 12.53 1.592 10.19 2.383 16.85 1.988 13.52 2.159 14.50 *The four-range and eight-range sections are in order from west to east. similar. Again the degree of accuracy obtained with four repHcations in four ranges would have been unattainable with five replications in 16 ranges. The oats variety test and strain test in 1921 were contiguous, oc- cupying 24 ranges, with 120 check plots of Kherson oats, or one in every sixth plot. The variability of these check plots in sections of Table 27. — Relation of Plot Variability to Size of Experiment Field. Check Plots in Oats Variety and Strain Test, 1921. No. of Size of field plots Yield Standard deviation bu. per acre bu. % Four ranges (1st) 20 35.81 4.75 13.26 Four ranges (2nd) 20 34.95 2.90 8.30 Four ranges (3rd) 20 38,14 4.21 11.04 Four ranges (4th) 20 39.60 4.66 11.77 Four ranges (5th) 20 38.91 4.14 10.65 Four ranges (6th) 20 40.31 4.14 10.27 Mean ^0 37.95 4.13 10.88 Eight ranges (1st) 40 35.38 3.96 11.19 Eight ranges (2nd) 40 38.87 4.50 11.58 Eight ranges (3rd) 40 39.60 4.21 10.62 Mean 40 37.95 4.22 11.13 Twelve ranges (1st) 60 36.30 4.25 11.71 Twelve ranges (2nd) 60 39.60 4.36 11.01 Mean 60 37.95 4.31 11.36 Twenty-four ranges 120 37.95 4.61 12.15 Experiments in Field Plot Technic 53 four, eight, and twelve ranges, and in the whole field of 24 ranges, is shown in Table 27. The variability of the whole field of 24 ranges was 12 per cent greater than the average variability of sections of four ranges each. In this case again, five replications in the larger field would have given less accurate results than four replications in the smaller. In each of the cases cited above a steady increase in variability is apparent as the size of the experiment field is increased. It is obvious that the substitution of 3-row plots with discarded borders for single rows will result in greater variability, and will require increased rep- lication for the same degree of accuracy. From the foregoing statements it will be clear that the number of replications necessary for a given degree of accuracy may vary con- siderably with conditions. The number to be used in any specific ex- periment should be determined from the variability of the field in question and the degree of accuracy required. The variability of the check plots is usually considered a measure of the variability of the field. But when the number of replications to be used or the extent of experimental error is determined from the variability of the check plots, it is assumed that the variability of different varieties of the same crop is approximately the same under the same conditions. This of course is not strictly true. The yield of two varieties may be deter- mined by very different factors, as has been stated, and their relative variability may also be quite different. The variability of 120 plots Table 28. — Son, Heterogeneity of an Experiment Field as Determined From Yields of Two Check Varieties. Oats Variety and Strain Tests. 1931. Number Average Probable error of a Check variety of plots yield Standard deviation single yield determination bu. bu. % bu. % Kherson 120 37.95 4.61 13.15 3.11 8.30 Red Rustproof 130 22.44 3.99 17.78 2.69 11.99 each of Kherson and Red Rustproof oats, grown side by side as check plots in the oats variety and strain test of 1921, illustrate the possibil- ity of a serious error in the use of the standard deviation of check plots as a measure of the variability of an experiment field. These determinations are shown in Table 28. The field would have been considered decidedly less variable if Kherson had been used as the check variety than if Red Rustproof had 54 Missouri Agr. Exp. Sta. Resi^arch Bulletin 49 been used. Both of these are standard recommended varieties for the region, though they differ decidedly in their characteristics. Both have been used frequently as check varieties at the Missouri station in past seasons. From the variability of the Kherson check plots the mean yield of four replicate plots in this experiment would be considered to have a probable error of 4.10 per cent ; from the Red Rustproof plots the same determination would be given a probable error of 6.00 per cent. A degree of precision for which we would assume four replica- tions necessary, judging from the Kherson check, v/ould require nine replications according to the yields of the Red Rustproof check. The importance of choosing a check variety typical of the va- rieties tested, if its variability is to be considered a criterion of the variability of the field, is obvious. Whether it is possble to choose a "typical variety" for the purpose, in the case of ordinary variety tests, remains to be seen. ADJUSTMENT OF YIELDS BY MEANS OF CHECK PLOTS Adjustment of plot yields by the use of check plots has been a common practice in field experiments during recent years. It is recognized that no experiment field is perfectly uniform in produc- tivity, and the attempt is made, by means of the check plot adjustment, to compensate the varieties or treatments which chance to be located on the less productive plots for the resulting loss in yield. The com- mon method, in variety tests, is to distribute over the field, as fre- quently as practicable, check plots planted to the same variety and similarly handled in every way. The variation in yield among these check plots is then considered a measure of the productivity of the soil. By various methods, differing only in detail, the yields of the test plots in parts of the field giving high check yields are reduced, and those of test plots in parts giving low check yields are increased, in proportion to the productivity of the soil, as indicated by the yields of neighboring check plots. Previous Investigation. — Several investigations of the effect of such adjustment on the variability of replicate plots have been re- ported. The majority of these have been conducted in connection with experiments of the type discussed in the preceding section, in which uniformly handled fields have been harvested in small sections. Cer- tain of these sections, or plots, have been considered check plots, and on the basis of their yields the yields of the remaining plots have been EXPE^RIMENTS IN FlELD PlOT TeCHNIC 55 adjusted. The reduction of variability of the adjusted plot yields is the measure of the efficiency of the method. Morgan" reports an experiment of this sort, in which 63 plots, planted first to wheat and then to fodder corn, in the same season, were used. The variability of the plot yields was steadily reduced as the number of check plots was increased. In a similar experiment reported by Lyon", in which Z7 replicate 1/100 acre plots of corn were harvested, the use of checks in every second or third plot was found to reduce variability, but they were of little value when farther apart. Montgomery" states that alternating check plots with test plots gives a high degree of accuracy, but the total number of plots required when this method is used is greater than when the same degree of ac- curacy is attained by the use of replication. Kiesselbach" reports a comprehensive trial of three methods of adjusting yields by means of check plots in a uniform field of 207 1/30-acre plots of Kherson oats. The effect on plot variability is shown in Table 29. Table 39. — Effect on Plot Variability op Adjusting Yields by Check Plots (Kiesselbach). Coefficient Method of of variability adjustment Actual Adjusted yields yields Alternate check plots. Correction based on average of two ad- jacent checks 7.85 7.01 Checks every third plot. Correction based on one adjacent check plot 7.79 7.35 Checks every third plot. Correction by progres- sive method, based on two nearest checks 7.87 6.57 From these results Kiesselbach concludes "The yield of system- atically distributed check plats cannot be regarded as a reliable meas- ure for correcting and establishing correct theoretical or normal yields for the intervening plats." It should be noted at this point that even if adjustment by check yields were found invariably effective in experiments of this sort, 56 Missouri Agr. Exp. Sta. Research Bulletin 49 its value in ordinary variety testing would not be definitely estab- lished. The practice involves not only the assumption that the yields of the check plots are a fair indication of the productivity of the in- tervening plots for the check variety, but the further assumption that different varieties respond similarly to differing growing conditions. Adjustment of yields should therefore give better results in such ex- periments as those cited above than it could be expected to give in actual variety tests. This point is well illustrated by observations reported by Salmon". Two varieties of barley, Gatami and Odessa, were grown side by side in fiftieth-acre plots in five distributed portions of a field. Gatami gave an average yield of 18.3 bushels per acre, with quite uniform yields in the five plots, as evidenced by their probable error of 0.68 bushel, while Odessa yielded 13.3 bushels per acre in the first plot, 6.35 bushels per acre in the second, and a negligible yield in the other three. Ob- viously the adjustment of the yield of either of these varieties on the basis of the other variety as a check, would enormously increase rather than decrease the experimental error. As Salmon points out, an error similar in kind though less in degree may occur commonly in variety tests, when the yields of varieties are determined by dif- ferent limiting factors. And if this is generally the case, adjustment by check yields will be of doubtful value, even if it were found to eliminate variability completely in uniform plot tests. There is a growing tendency, consequently, to discontinue the use of check plots for adjusting yields in variety tests, and to use them only to measure soil variability and to indicate the degree of error in yield determinations of the tested varieties. Adjustment of yields has never been as common in preliminary tests as in tests on larger plots, principally because of the great amount of computation neces- sary in adjusting the yields of ten or twenty replicate rod-rows of a large number of varieties, and because the yield of a single rod-row, exposed to varying competition and materially affected by small me- chanical errors, is at best a very unreliable measure of productivity on which to base the adjustment of the yields of several other plots. Experimental Results. — It would of course be very desirable to use check plots for reducing plot variability, if the method could be relied on, because of the economy of the practice. The only certain method of reducing plot variability is by means of replication, and it may be considered a fairly general rule that the variability of plots on a given field, as measured by the standard deviation or the prob- able error, will in general be reduced by replication in proportion to the square root of the number of replications. In other words, the Experiments in Field Plot Technic 57 variability of the mean of 16 replicate plots will be about half that of the mean of 4 replicate plots. Now the maximum use of check plots, that is, the practice of alternating check plots and test plots, requires the same land and labor as would be required by doubling the num- ber of replications, if no check plots were used. As doubling the number of replications will in general give a standard deviation about equal to the original standard deviation divided by the square root of 2, it will reduce variability about 30 % | — = =.7071 | . If alternat- ing with check plots will consistently reduce variability more than 30 per cent it will be generally a more economical way to control error. Similarly, the use of check plots in every third plot requires as much land as would be required by increasing the number of replications by 50 per cent (using three replications instead of two, or fifteen instead of ten). From this relation the reduction of variability necessary if this practice is to equal replication in effectiveness can be easily com- puted. Such determinations for check plots at various intervals are shown in Table 30. Table 30. — Reduction of Variability by the Use of Check Plots Equivalent TO That Probably Attainable With the Same Number OF Plots by Replication. Reduction in standard deviation to Distribution of Equivalent increase in be expected by such check plots number of replications increase in replication % % Alternate plots 100.00 29.29 Every third plot 50.00 18.35 Every fourth plot 33.33 13.50 Every fifth plot 25.00 10.55 Every sixth plot 20.00 8.71 Every seventh plot 16.67 7.41 Every eighth plot 14.29 6.47 Every ninth plot 12.50 5.75 Every tenth plot 11.11 5.12 If protected single-row or 3-row plots are used in preliminary experiments a more reliable measure of soil productivity is available, and consequently the adjustment of yields is more likely to be of value, than when unprotected single-row plots are used. By the use of planting plans of the sort employed in these experiments, it is pos- 58 Missouri Agr. Exp. Sta. Research Bulletin 49 sible to adjust the yields by a somewhat shortened method. If adjust- ment of yield is effective in reducing plot variability in this sort of test it can be accomplished with but little increase in labor. In each of the tests reported in this paper a trial of the effectiveness of adjust- ing yields by means of check plots was made, the criterion of accuracy being in each case the variability of the yields of the replicate plots of each variety. Since the number of replicate plots was only three or four the average deviation was determined instead of the stand- ard deviation. Method Used in Adjusting Yields. — The method employed in ad- justing yields may be described as follows: The average yield of all check plots and the relative yield of each check plot in terms of this average (that is, the quotient obtained by dividing the yield of the in- dividual check plot by the average yield of all check plots) were de- termined. The relative yield of each check plot, expressed in per- centage of the mean check yield, is designated hereafter as the "plot value" of that check plot. When the average yield of all check plots is 25 bushels per acre, the plot value of a check plot yielding 30 bushels per acre is 120 per cent — in other words it is 20 per cent more pro- ductive than the average. Now assuming gradual change in the pro- ductivity of the soil between check plots, each test plot is assigned a plot value by interpolation. The adjusted yield of each plot is then determined by dividing the actual yield by the plot value. The short method for adjusting yields, referred to above, is based on the fact that the varieties occur in the same order in each series. Thus in the field diagrammed in figure 1, the following se- quence of plots occurs in each of the four series : ck 1 17 33 49 65 81 ck Now if the average yield of the four check plots adjoining variety 1, and the average yield of the four check plots adjoining variety 81 are each given a plot value, corresponding plot values for the mean yields of varieties 1, 17, 33, 49, 65, and 81 may be interpolated, and the mean yields may be adjusted in one operation. The same method may be used, of course, regardless of the number of replications. The result will not be exactly the same as that of averaging the adjusted yields determined individually, but will in most cases approximate it closely, the slight dift'erence being caused by the disproportion of yield and plot value in the plots averaged. It is doubtful that either meth- od is consistently more accurate than the other. When the check plot yield is used in the adjustment of the yields of other plots it is of course essential that it should be a reliable de- termination, not unduly affected by factors not affecting the neighbor- Experiments in Field Plot Technic 59 ing plots. For example if the yield of a check plot is reduced 20 per cent by a poor stand, the adjusted yields of neighboring plots will be increased to the same extent as if the check plot yield had been low be- cause of poor soil, and will consequently be considerably higher than they should be. It is important therefore that conditions be made as fa- vorable as possible for accurate yield testing when this method is used. One cause for poor results in the adjustment of yield in some of the experiments reported in this paper was failure to protect the outside strip of check plots by means of border rows, in a few of the tests, be- Tabi,e 31. — Relative Variability of Actual and Adjusted Yields. Average Deviation in Percentage of Yield. — Barley Variety Test 1919. Average deviation Planting Actual yields Adjusted yields number Variety 3 interior rovers 5 rows 3 interior rows 5 rows % % % % 1 Hanna 906 19.81 17.82 13.15 10.80 3 Steigum 907 15.17 18.79 13.48 8.40 3 Luth 908 29.97 28.17 5.51 4.62 4 Eagle 913 26.14 29.79 9.71 12.98 6 Servian 915 18.37 17.97 7.36 5.59 7 Odessa 916 2.31 4.33 23.99 17.01 8 Lion 923 14.65 12.10 11.37 11.03 10 Horn 926 4.08 2.00 16.45 12.74 11 Odessa 927 13.62 9.16 21.62 13.76 13 Summit 929 5.28 6.45 14.23 11.59 13 Mariout 932 11.02 11.57 18.68 14.31 14 Odessa 934 13.73 13.91 11.18 10.31 15 Peruvian 935 13.25 17.87 12.42 16.82 16 Trebi 936 11.27 12.53 18.78 18.28 18 Oderbrucker 940 10.77 14.46 13.60 15.98 19 Prankish 953 20.53 19.65 22.63 18.49 20 Manchuria 956 6.88 6.33 13.89 10.68 21 Oderbrucker 957 17.88 13.62 1.97 3.37 22 Manchuria x Champion 39.47 39.19 21.93 20.35 of Vermont 33 Luth 972 16.77 18.61 7.05 7.48 24 Red River 973 13.94 11.02 12.37 12.33 25 Featherston 1118 21.40 20.89 8.47 13.39 26 Featherston 1119 16.59 15.25 4.78 12.26 27 Featherston 1120 15.91 13.64 2.48 6.44 28 Hanna x Champion of Vermont 1121 16.00 16.81 28.36 28.50 29 Manchuria 1125 6.79 14.42 7.78 1.55 30 Malting 1129 12.86 10.40 5.40 9.02 Mean 15.35 15.44 12.91 12.15 60 Missouri Agr. Exp. Sta. Research Bulletin 49 cause of lack of space. The check plots growing on the border of the field were materially reduced in yield, in some cases, notably the oats strain test of 1919 and the wheat variety test of 1921. In these cases the variability of the actual and adjusted yields has been computed both for all series and for the remaining series when the one affected by an unreliable check is discarded. Relative Variability of Actual and Adjusted Yields. — The relative variability of actual and adjusted yields of both 3-row and 5-row plots in the barley variety test is shown in Table 31. In this test there were three replications, and the check variety was Oderbrucker, in every Tab i,E 32.— Relative Variability OF Actual and Adjusted Yields. Average Deviation in Percentage of Yield Oats Variety Test 1919. Average Deviation Planting 3 Series 4 : Series number Variety (3 interior rows) (3 interior rows) Actual Adjusted Actual Adjusted yields yields yields yields % % % % 1 A. sterilis nigra 4.32 1.46 9.18 5.02 2 Black Mesdag 9.03 9.69 7.29 12.90 3 C. I. 602 13.72 16.00 16.30 13.63 3 C. I. 603 4.72 3.09 5.84 3.88 5 C. I. 620 4.73 10.14 11.24 13.67 6 Early Champion 18.63 15.18 14.97 14.65 7 Early Gothland 14.20 4.67 11.55 4.18 8 Garton 473 5.99 6.25 8.42 9.42 9 Garton 585 14.08 19.44 16.92 19.95 10 Golden Giant 9.44 14.31 14.40 15.09 11 Irish Victor 9.69 3.29 7.72 16.40 12 Japanese Selection 6.87 4.71 11.85 5.20 13 June 18.37 11.19 17.53 10.37 14 Kherson Selection 17.01 9.20 15.06 20.36 15 Fulghum 9.69 11.36 13.06 17.32 16 Lincoln 21.07 12.54 16.56 11.83 17 Monarch 6.12 4.55 9.06 33.36 18 North Finnish 8.69 5.17 7.84 27.03 19 Scottish Chief 5.05 4.28 5.10 15.42 20 Sparrow bill (Missouri) 10.98 10.82 12.38 13.15 21 Sparrow bill (Cornell) 4.45 3.25 12.11 3.85 22 Tobolsk 1 6.17 3.85 13.92 5.38 23 Tobolsk 2 11.56 9.24 20.35 13.96 24 White Tartar 10.94 4.75 9.51 4.54 Mean 10.23 8.27 12.01 12.94 Experiments in Field Plot Technic 61 sixth plot. As a result of the adjustment of yields, the average devia- tion of 3-row plots was reduced from 15.35 per cent to 12.91 per cent, a reduction of 16 per cent, and that of 5-row plots from 15.44 per cent to 12.15 per cent, a reduction of 21 per cent. The relative variability of actual and adjusted yields in the oats variety test of 1919 is shown in Table 32. In this field the check. Red Rustproof, was in every ninth plot. When the series affected by the faulty check yields of the border plots is included the variability of the adjusted yields is slightly higher than that of the actual yields, but when this series is discarded the average variability as measured by the mean deviation is reduced 19 per cent. It might be expected that the oats strains grown on the same field would show a greater reduction of variability than the varieties, since practically all of them were of the same variety as the check, and since Table 33. — Relative Variability of Actual and Adjusted Yields. Average Deviation in Percentage of Yield. Oats Strains Test 1919. Planting Accession number number Average deviation Actual yields Adjusted yields interior rowrs 5 rows 3 interior rows 5 rows % % % % 1 0119 10.30 7.75 11.23 8.81 2 0120 4.70 6.58 3.01 1.76 3 0121* 5.76 3.25 4.57 4.14 4 0122 4.62 3.52 6.46 3.82 5 0123 9.91 8.25 11.47 9.62 6 0125 3.18 3.34 5.39 6.60 7 0126 7.62 5.95 10.56 16.58 8 0127* 6.76 5.09 6.92 9.85 9 0124* 6.13 6.34 4.92 4.59 10 0133 7.07 4.77 3.92 5.36 11 0128 4.17 3.56 3.58 3.36 12 0129 5.03 7.07 5.94 6.35 13 0130 4.20 2.62 6.74 9.72 14 0131 3.59 2.59 4.98 2.94 15 0132 7.38 5.81 12.38 12.08 Mean 5.96 5.10 6.80 7.04 * Not taxonomically Red Rustproof. the check plots were more frequent, being in every sixth plot. The results of adjusting yields in this test, both for protected 3-row plots and for unprotected 5-row plots in four series are shown in Table 33. Contrary to expectation, the variability was not reduced by adjustment 62 Missouri Agr. Exp. Sta. 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Ti- m\dt^ooo\Oi-itsifo-*u-i\or^ooo\ Or-icM<^Thvo*ot^ooo\0'-icMfOTHo\o vo vo^ovov£)\o^^t^r^^Nt^t^^^^^t^^N oooooooooooocoooooooavO^ONa\a\Cha\ ) CM VO .-H ro CM I J \Q \^ \0 ^ VO >r^ioi^^fOOPo^»-HOs^' )V0CMOCMV0'^CM^O^i-ir^vOa\I^mTl-Ot^0000c^^^OO0s0NV0^ir3a\0N00v0»-Hf^» !OOt^>o"^t^oot^oooocM>o>ovoc:\fo>-imo\o\ ^O^0OOTJ-0^^HrH0\^0^H,-^.-l•-l^c^^0^CMO^'^f^0000CMPOO^00lr>a^0^l 1 1-.. CO in oo ■* t>. I ONfMVO'-'OOTt'VO^HONCO'^LnVO-^vOro'^OvC^^CvlmOOOOOroOPOtOTl-, 1 CM O M- CM ■'I- 00 < r-1 VO CM I iroCMCM^'^-iOCM'-t'-iI^i o o" -« ; o -^1- 1^ oc P30 .-H CM o ra c O C 4) rt rt rt -Ul -^ o u l^ c C I* . C N rt >» X >^ C , Q .-H O (13 n] 03 rt ' >. o o ooUW oooodoOoo .— OJ cu (LI a; 11 a! r! rOTj-mvOl^COON O'-HCMPOTj-u-ivOt^OOaNO'-'lM*"'^*^ ZZ V t> V " -a -o T3 -a T3 -a -a T3 -a 13 X g' rjCcsccEoooooooooo 13 Ti g" o 1— ' 5j jj wiWibiibcbehcbcbfibfibiSWibcbiibo CMCMCMCMCv) CMCMCMCMCM' Experiments in Field Plot Technic 65 Table. 36— Relative Variability of Actual and Adjusted Yields. Average Deviation in Percentage of Yield. Wheat Mixture Test 1921 Average Deviation Planting Actual yields Adjusted yields number Variety (3 interior rows) (3 interior rows) 1 Fulcaster 9.67 16.90 2 Harvest Queen 9.35 21.47 3 Mixture No. 1 6.12 20.11 4 Michigan Wonder 7.88 20.51 5 Nigger 2.33 20.16 6 Michigan Wonder No. 31 4.93 13.86 7 Michigan Wonder No. 54 12.96 16.03 8 Mixture No. 2 15.38 17.86 9 Michigan Wonder No. 96 4.99 13.88 10 Michigan Wonder No. 209 5.30 14.83 11 Beechwood Hybrid No. 12 9.04 11.01 13 Beechwood Hybrid No, . 85 14.98 15.49 13 Mixture No. 3. 16.76 10.47 14 Beechwood Hybrid No . 87 10.16 11.94 15 Beechwood Hybrid No. 207 20.80 11.81 16 Michigan Wonder No. 221 7.13 8.90 17 Kanred 10.09 12.86 18 Mixture No. 4 10.39 8.44 19 New York 123-32 16.73 12.09 20 Red Rock 14.04 10.68 21 Red Hussar 12.71 17.42 22 Turkey (Kansas) 17.32 13.74 23 Mixture No. 5 2.87 12.73 24 Michigan Amber 3.39 10.71 25 Nigger 4.09 10.47 26 Fulcaster (Co-op) 2.09 14.25 27 Fulcaster (Outl) 11.97 17.18 28 Mixture No. 6 11.19 7.75 29 Fulcaster (Blazier) 11.41 6.77 30 Fulcaster (Cowles) 9.09 14.11 Mean 9.84 13.81 32 of other varieties. The yields were adjusted by means of each check variety separately, to determine the relation between the ef- fectiveness of yield adjustment and the similarity of the check to the tested variety. The results of this adjustment on plot variability are shown in Tables VI and 38. The variability of the yields of the Red Rustproof strains was somewhat reduced (6 per cent) by adjustment according to the yields 66 Missouri Agr. Exp. Sta. Research Bulletin 49 Tabli; 37. — Relative Variability of Actual and Adjusted Yields. Average Deviation in Percentage of Yield. Oats Variety Test 1931 Average deviation Planting Actual yields Adjusted yields number Variety (3 interior (3 interior rows) rows) (Kherson) (Red Rustproof) % % % 65 Burt 10.23 11.54 11.00 66 Canadian 9.29 8.93 18.37 67 C. I. 603 9.21 4.94 13.89 68 Culberson 6.46 8.80 4.44 69 Danish Island 10.53 8.83 12.56 70 Early Dakota 9.33 7.96 11.45 71 Early Gothland 10.00 19.16 14.69 72 Carton 748 14.35 13.36 14.77 73 Green Russian 9.75 11.23 13.75 74 Irish Victor 9.43 8.07 15.99 75 Joanette 30.75 29.36 26.94 76 Fulghum 043 5.19 8.50 8.99 77 Monarch 4.76 6.36 8.54 78 Monarch Selection 2.89 5.74 11.55 79 Scottish Chief 10.95 15.01 8.66 80 Silvermine 050 11.24 9.88 9.21 81 Silvermine Selection 11.25 16.14 3.16 83 Sparrowbill (C) 23.93 23.03 25.23 83 Sterilis Selection 8.02 7.30 9.17 84 Storm King 11.68 13.94 13.15 85 Swedish Select 057 14.48 14.89 11.80 86 Fulghum 065 8.81 11.04 9.41 87 Fulghum 0113 22.19 11.18 15.85 88 Silvermine 0115 8.38 6.29 3.59 89 Silvermine 0117 6.90 8.95 9.69 90 Fulghum 0124 5.17 3.38 7.89 91 Fulghum 0145 9.81 8.63 15.66 92 Fulghum 0149 10.19 10.77 15.70 93 Fulghum 0151 10.85 13.71 10.80 94 Fulghum 0153 9.07 14.59 19.61 95 Silvermine 0165 5.63 11.33 4.62 96 Swedish Select 0165 16.74 14.03 8.74 Mean 10.86 11.43 12.15 of the Red Rustproof check, but was slightly increased (2 per cent) when the Kherson check was used. On the other hand, the variability of the yields of the Kherson strains, though not reduced by either check, was increased only 4 per cent by the Kherson check, while it was in- creased 48 per cent by the Red Rustproof check. Neither check was effective in adjusting the yields of the other varieties, the Kherson Experiments in Field Plot Technic 67 Table 38. — Relative Variability of Actual and Adjusted Yields. Average Deviation in Percentage of Yield. — Oats Strain Test 1921 (Red Rustproof and Kherson) Red Rustproof strains Kherson strains Average deviation Average deviat on u v E 3 Strain 3.2 ^1 Adjusted (3 interior yields rows) V e 3 bo Strain a ; 3 2 " ^> Adjusted yields (3 interior rows) (Kher- son) . . (Red Rust- proof) (Kher- son) . . (Red Rust- proof) % % % % % % 1 066 18.13 15.48 13,04 2 023 15.80 7.59 12.93 3 067 12.89 14.19 11.36 4 040 3.86 5.59 10.45 5 068 23.14 21.34 12.47 6 041 9.50 5.82 4.07 7 069 21.55 20.54 11.70 8 052 3.46 2.83 10.49 9 072 14.29 12.26 10.34 10 053 6.26 5.97 10.14 11 074 12.18 17.23 13.94 12 079 11.49 9.91 10.20 13 075 13.40 18.28 18.80 14 080 1.72 7.02 13.20 15 0118 28.77 32.06 26.92 16 082 6.19 8.74 15.01 IS 0119 10.32 13.47 13.62 17 083 5.31 5.88 9.26 20 0120 7.28 6.11 12.32 19 085 8.69 10.65 7.30 22 0122 17.16 12.32 14.20 21 086 11.73 7.45 8.45 24 0125 10.91 11.52 8.40 23 fixture** • 4.87 3.84 9.19 26 0126 10.41 10.24 4.66 25 088** 13.04 13.79 9.16 28 0128 14.48 17.36 2.76 27 089 4.69 6.77 12.89 30 0129 7.89 6.31 7.44 29 090 2.84 4.85 10.64 32 0130 7.99 11.78 9.17 31 091 12.46 14.67 10.84 33 0131 12.43 13.96 13.23 34 094 4.59 6.43 6.57 35 0132 17.77 14.67 12.11 36 095 4.36 4.96 14.62 37 0133 14.07 11.63 13.55 38 096 4.39 7.71 4.66 39 0134 29.91 30.37 29.50 40 097 5.53 6.97 11.80 41 0135 14.36 17.58 13.11 42 098 9.09 10.03 13.18 43 0136* 7.80 7.59 12.69 44 099 6.89 6.26 10.20 45 0141 12.58 13.30 11.11 46 0100 6.90 4.65 8.55 47 0163 2.70 1.82 14.28 48 0155 12.75 4.49 23.56 50 0169 21.95 17.79 23.03 49 0157 6.34 7.40 14.18 52 0181 9.95 7.62 9.69 51 0158 10.81 12.24 6.26 54 0182 26.12 21.76 20.84 53 0159 6.33 10.82 8.26 56 0183* 4.52 5.51 8.99 55 0160 4.98 6.12 12.52 58 0383 10.10 15.60 20.18 57 0161 5.55 9.19 9.27 60 0391 9.55 11,37 6.47 59 0162 11.28 13.38 9.47 62 0394 13.03 11.52 10.29 61 0167 2.65 3.37 4.41 64 0395 8.69 11.40 17.96 63 0174 10.74 8.96 15.67 W ean 14.47 14.70 13.55 Mean 7.16 7.44 10.59 • Not taxonomically Red Rustproof. Excluded from average. ** Not taxonomically Kherson. Excluded from average. ♦••Mixture of strains 082, 094, 0100, 0174. check increasing their variability 7 per cent, and the Red Rustproof check 20 per cent. These results indicate the importance of using a check variety typical of the varieties tested, when adjustment of yields is to be made ; and the danger of increasing rather than decreas- 68 Missouri Agr. Exp. Sta. Research Bulletin 49 ing error by this practice when the tested varieties are quite different in habit from the check variety. The use of an unsuitable check variety not only increases the margin of error, but it may cause very deceptive comparative results. For example, the average yields of the Kherson strains 0155 and 0157, unadjusted and adjusted according to the yields of both check va- rieties, are shown below : Strain Method 0155 0157 Yield Average Deviation Yield Average Deviation Unadjusted Adjusted by Kherson check Adjusted by Red Rustproof check 37.50 34.50 39.94 12.75 4.49 23.56 43.69 43.69 39.38 6.34 7.40 14.18 The 17 per cent advantage in yield of strain 0157 is increased to 27 per cent by the Kherson adjustment, and since the variability of the replicate yields is reduced by the adjustment we may fairly as- sume that the latter is the more reliable figure. But when the Red Rustproof check is used for adjusting yields, the advantage of strain 0157 disappears entirely. The inaccuracy of the yields adjusted by Red Rustproof is indicated by the increase in plot variability result- ing from this adjustment. Thus the adjustment of yields by means of check plots may mask considerable differences in yields between the varieties under test. Although Kherson and Red Rustproof are decidedly different in type, both are commonly grown in Missouri, and both have been used frequently here as check varieties in oats variety tests. It is interesting Tabi:,e 39. — Relative Variability of Actual and Adjusted Yields of Kherson AND Red Rustproof Oats, Each in 120 Distributed Plots. Oats Variety and Strain Tests 1921. Variety Kherson Red Rustproof Yield Actual Adjusted Standard deviation Actual Adjusted yield yield % % 37.95 39.04 12.15 20.79 22.44 22.80 17.78 19.92 Experiments in Field Plot Technic 69 to determine the effect on variability of adjusting the yields of the 120 plots of Kherson, on the basis of those of the 120 plots of Red Rustproof adjoining them, and those of the 120 plots of Red Rustproof, on the basis of the yields of the adjoining Kherson plots. In this adjustment the yield of each plot is divided by the plot value of the adjoining plot, and the method corresponds to method II used by Kiesselbach in the experiment cited above (see Table 29). The results of the yield adjustment are shown in Table 39. The adjustment of plot yields by means of check plots of a va- riety distinctly different in type resulted in a decided increase in plot variabihty, even though the plot values used were determined in each case by the yield of the immediately adjacent plot. If the yields of the Kherson and the Red Rustproof plots had been perfectly ac- curate measures of the productivity of the soil, the plot values of the adjacent plots would have been almost the same in each of the 120 locations, and the adjustment of the yields of either variety by those of the other would have reduced variability almost to zero. Instead, variability was actually and very decidedly increased, because the sec- tions of the field which gave relatively high yields of Kherson, gave relatively low yields of Red Rustproof, and vice versa, in many cases. In fact, there was very little relation between the productivity of a portion of the field as determined by a Kherson check, and the pro- 60 to 70 70 to 80 80 to 90 90 to 100 100 to 110 110 to 120 120 to 130 130 to 140 140 to 150 150 to lee 160 to 170 170 to 180 Total iH tH 1-1 iH l-H ■-1 iH w N N N (M W (M